Literal Equations and Formula Rearrangement

Overview of Literal Equations

• Literal equations are equations that contain multiple variables rather than mostly numbers.
• The goal is to isolate a specific variable in terms of the other variables using standard inverse operations.
• Rearranging a formula is efficient for repetitive calculations, allowing for direct input into the desired variable's expression.

Temperature Conversion Formulas

• The formula to convert Fahrenheit to Celsius is: $c = \frac{5}{9}(f - 32)$.
• To solve for $f$ (Fahrenheit) in terms of $c$ (Celsius):
  • Multiply both sides by the reciprocal of the fraction: $\frac{9}{5}c = f - 32$.
  • Add $32$ to both sides to isolate the variable: $f = \frac{9}{5}c + 32$.
• Note: Terms involving variables (like $c$) and constants (like $32$) are not like terms and must be kept separate with an operator.

Geometric and Algebraic Formulas

• To rearrange the area of a triangle formula, $a = \frac{1}{2}bh$, for the base ($b$):
  • Multiply by $2$ to remove the fraction: $2a = bh$.
  • Divide by the height ($h$) to isolate the base: $b = \frac{2a}{h}$.
• For complex algebraic expressions, such as solving $2m - t = sm + 5$ for $s$:
  • Subtract constants first: $2m - t - 5 = sm$.
  • Divide by the coefficient variable ($m$) to isolate the target: $s = \frac{2m - t - 5}{m}$.